Math 1550 Fall 2005 Section 31 P. Achar Summary: Math 1550 Fall 2005 Section 31 P. Achar Extra Credit Due: December 6, 2005 The dimension of a geometric object is the number of coordinates it takes to specify a location in the object. For example, the surface of a sphere (such as the surface of the earth) is 2-dimensional, because you can specify a location with two numbers: its latitude and longitude. On the other hand, a solid sphere is 3- dimensional: to identify a point within the earth, you must give its latitude, longitude, and depth from the surface. The way in which one speaks of the "size" of an object depends on its dimension: 1-dimensional objects have length, 2-dimensional things have area, and 3-dimensional things have volume. It is possible to study the geometry of objects with more than three dimensions, even though we obviously can't imagine or draw pictures of such objects. There aren't any ordinary English words to describe things in more than three dimensions, however, so what mathematicians usually do is just use 3-dimensional terminology, but with added numerical prefixes to indicate the dimension. For instance, there is no English word for the "size" of a 4-dimensional object (which would be measured in cm4 or in4 ), so mathematicians just call it "4-volume." You can also use "1-volume" as a synonym for "length," and "2-volume" as a synonym for "area." Circles and spheres are part of a family of shapes in all different dimensions. The goal of this problem is to Collections: Mathematics